We prove (and weighted ) bounds for singular integrals of the form
where cos if is odd, and sin if is even, and where BMO. Even in the case that is smooth, the theory of singular integrals with "rough" kernels plays a key role in the proof. By standard techniques, the trigonometric function can then be replaced by a large class of smooth functions . Some related operators are also considered. As a further application, we prove a compactness result for certain layer potentials.
Cite this article
Dorina Mitrea, On singular integrals of Calderón-type in , and BMO. Rev. Mat. Iberoam. 10 (1994), no. 3, pp. 467–505DOI 10.4171/RMI/159